H-mode transitions and limit cycle oscillations from mean field transport equations

Staebler, Gary M.; Groebner, Richard J.

doi:10.1088/0741-3335/57/1/014025

Title: H-mode transitions and limit cycle oscillations from mean field transport equations

Abstract

The mean field toroidal and parallel momentum transport equations will be shown to admit both onestep transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExB velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. As a result, the transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.

Authors:

Staebler, Gary M. ^[1]; Groebner, Richard J. ^[1]

General Atomics, San Diego, CA (United States)

Publication Date:: Fri Nov 28 00:00:00 EST 2014

Research Org.:: General Atomics, San Diego, CA (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE)

OSTI Identifier:: 1356339

Grant/Contract Number:: FC02-04ER54698

Resource Type:: Accepted Manuscript

Journal Name:: Plasma Physics and Controlled Fusion

Additional Journal Information:: Journal Volume: 57; Journal Issue: 1; Journal ID: ISSN 0741-3335

Publisher:: IOP Science

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; mean field transport; limit cycle oscillations; H-mode transitions

Citation Formats


                    Staebler, Gary M., and Groebner, Richard J. H-mode transitions and limit cycle oscillations from mean field transport equations.  United States: N. p., 2014. 
Web.  doi:10.1088/0741-3335/57/1/014025.

Copy to clipboard


                    Staebler, Gary M., & Groebner, Richard J. H-mode transitions and limit cycle oscillations from mean field transport equations.  United States.  https://doi.org/10.1088/0741-3335/57/1/014025

Copy to clipboard


                    Staebler, Gary M., and Groebner, Richard J. Fri .  
"H-mode transitions and limit cycle oscillations from mean field transport equations".  United States.  https://doi.org/10.1088/0741-3335/57/1/014025.  https://www.osti.gov/servlets/purl/1356339.

Copy to clipboard


                    
@article{osti_1356339,

  title        = {H-mode transitions and limit cycle oscillations from mean field transport equations},

  author       = {Staebler, Gary M. and Groebner, Richard J.},

  abstractNote = {The mean field toroidal and parallel momentum transport equations will be shown to admit both onestep transitions to suppressed transport (L/H) and limit cycle oscillations (LCO). Both types of transitions are driven by the suppression of turbulence by the mean field ExB velocity shear. Using experimental data to evaluate the coefficients of a reduced transport model, the observed frequency of the LCO can be matched. The increase in the H-mode power threshold above and below a minimum density agrees with the trends in the model. Both leading and lagging phase relations between the turbulent density fluctuation amplitude and the ExB velocity shear can occur depending on the evolution of the linear growth rate of the turbulence. As a result, the transport solutions match the initial phase of the L/H transition where the poloidal and ExB velocities are observed to change, and the density fluctuations drop, faster than the diamagnetic velocity.},

  doi          = {10.1088/0741-3335/57/1/014025},

  journal      = {Plasma Physics and Controlled Fusion},

  number       = 1,

  volume       = 57,

  place        = {United States},

  year         = {Fri Nov 28 00:00:00 EST 2014},

  month        = {Fri Nov 28 00:00:00 EST 2014}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1088/0741-3335/57/1/014025

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 16 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Role of Zonal Flow Predator-Prey Oscillations in Triggering the Transition to H-Mode Confinement
journal, April 2012

Schmitz, L.; Zeng, L.; Rhodes, T. L.
Physical Review Letters, Vol. 108, Issue 15
DOI: 10.1103/PhysRevLett.108.155002

Drift wave based modelling of poloidal spin-up precursor and stepwise expansion of transport barriers
journal, July 2001

Staebler, G. M.; Waltz, R. E.; Kinsey, J. E.
Nuclear Fusion, Vol. 41, Issue 7
DOI: 10.1088/0029-5515/41/7/310

Fluctuation level bursts in a model of internal transport barrier formation
journal, March 1999

López-Bruna, D.; Newman, D. E.; Carreras, B. A.
Physics of Plasmas, Vol. 6, Issue 3
DOI: 10.1063/1.873325

Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices
journal, May 1997

Burrell, K. H.
Physics of Plasmas, Vol. 4, Issue 5
DOI: 10.1063/1.872367

Constraints on theories provided by fast time response measurements across the L to H transition on DIII-D
journal, August 1996

Burrell, K. H.; Carlstrom, T. N.; Coda, S.
Plasma Physics and Controlled Fusion, Vol. 38, Issue 8
DOI: 10.1088/0741-3335/38/8/028

Bifurcation theory of poloidal rotation in tokamaks: A model for L-H transition
journal, November 1989

Shaing, K.; Crume, E.
Physical Review Letters, Vol. 63, Issue 21
DOI: 10.1103/PhysRevLett.63.2369

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
journal, January 1982

Frieman, E. A.
Physics of Fluids, Vol. 25, Issue 3
DOI: 10.1063/1.863762

Modifications in turbulence and edge electric fields at the L–H transition in the DIII‐D tokamak
journal, August 1991

Doyle, E. J.; Groebner, R. J.; Burrell, K. H.
Physics of Fluids B: Plasma Physics, Vol. 3, Issue 8
DOI: 10.1063/1.859597

Neoclassical quasilinear transport theory of fluctuations in toroidal plasmas
journal, January 1988

Shaing, K. C.
Physics of Fluids, Vol. 31, Issue 8
DOI: 10.1063/1.866626

Transport processes and entropy production in toroidally rotating plasmas with electrostatic turbulence
journal, February 1997

Sugama, H.; Horton, W.
Physics of Plasmas, Vol. 4, Issue 2
DOI: 10.1063/1.872099

Poloidal momentum transport due to drift-waves in toroidal geometry
journal, March 2004

Staebler, G. M.
Physics of Plasmas, Vol. 11, Issue 3
DOI: 10.1063/1.1647564

Moment equation approach to neoclassical transport theory
journal, January 1978

Hirshman, Steven P.
Physics of Fluids, Vol. 21, Issue 2
DOI: 10.1063/1.862195

The effect of the radial electric field on the L–H transitions in tokamaks
journal, March 1992

Rozhansky, V.; Tendler, M.
Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7
DOI: 10.1063/1.860463

Mean and Oscillating Plasma Flows and Turbulence Interactions across the $L − H$ Confinement Transition
journal, February 2011

Conway, G. D.; Angioni, C.; Ryter, F.
Physical Review Letters, Vol. 106, Issue 6
DOI: 10.1103/PhysRevLett.106.065001

First Evidence of the Role of Zonal Flows for the $L − H$ Transition at Marginal Input Power in the EAST Tokamak
journal, September 2011

Xu, G. S.; Wan, B. N.; Wang, H. Q.
Physical Review Letters, Vol. 107, Issue 12
DOI: 10.1103/PhysRevLett.107.125001

Observation of the $L − H$ Confinement Bifurcation Triggered by a Turbulence-Driven Shear Flow in a Tokamak Plasma
journal, March 2014

Yan, Z.; McKee, G. R.; Fonck, R.
Physical Review Letters, Vol. 112, Issue 12
DOI: 10.1103/PhysRevLett.112.125002

Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field
journal, January 1973

Catto, Peter J.
Physics of Fluids, Vol. 16, Issue 10
DOI: 10.1063/1.1694200

Gyrokinetic theory and simulation of angular momentum transport
journal, December 2007

Waltz, R. E.; Staebler, G. M.; Candy, J.
Physics of Plasmas, Vol. 14, Issue 12
DOI: 10.1063/1.2824376

Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio
journal, September 1997

Houlberg, W. A.; Shaing, K. C.; Hirshman, S. P.
Physics of Plasmas, Vol. 4, Issue 9
DOI: 10.1063/1.872465

New Paradigm for Suppression of Gyrokinetic Turbulence by Velocity Shear
journal, January 2013

Staebler, G. M.; Waltz, R. E.; Candy, J.
Physical Review Letters, Vol. 110, Issue 5
DOI: 10.1103/PhysRevLett.110.055003

A new paradigm for E × B velocity shear suppression of gyro-kinetic turbulence and the momentum pinch
journal, September 2013

Staebler, G. M.; Candy, J.; Waltz, R. E.
Nuclear Fusion, Vol. 53, Issue 11
DOI: 10.1088/0029-5515/53/11/113017

Neoclassical ion transport in rotating axisymmetric plasmas
journal, January 1985

Hinton, F. L.; Wong, S. K.
Physics of Fluids, Vol. 28, Issue 10
DOI: 10.1063/1.865350

Fuel ion rotation measurement and its implications on H-mode theories
journal, July 1994

Kim, J.; Burrell, K. H.; Gohil, P.
Plasma Physics and Controlled Fusion, Vol. 36, Issue 7A
DOI: 10.1088/0741-3335/36/7A/025

Gyro-Landau fluid equations for trapped and passing particles
journal, October 2005

Staebler, G. M.; Kinsey, J. E.; Waltz, R. E.
Physics of Plasmas, Vol. 12, Issue 10
DOI: 10.1063/1.2044587

Works referencing / citing this record:

Magnetic-confinement fusion
journal, May 2016

Ongena, J.; Koch, R.; Wolf, R.
Nature Physics, Vol. 12, Issue 5
DOI: 10.1038/nphys3745

H-mode access and the role of spectral shift with electrode biasing in the TCABR tokamak
journal, July 2018

Grenfell, G. G.; Nascimento, I. C.; Oliveira, D. S.
Physics of Plasmas, Vol. 25, Issue 7
DOI: 10.1063/1.5029561

Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST)
journal, December 2019

Ye, K. X.; Zhang, T.; Xiang, H. M.
Physics of Plasmas, Vol. 26, Issue 12
DOI: 10.1063/1.5119039

Similar Records in DOE PAGES and OSTI.GOV collections:

The role of zonal flows and predator–prey oscillations in triggering the formation of edge and core transport barriers

Journal Article Schmitz, Lothar ; Zeng, Lei ; Rhodes, Terry L. ; ... - Nuclear Fusion

Here, we present direct evidence of low frequency, radially sheared, turbulence-driven flows (zonal flows (ZFs)) triggering edge transport barrier formation preceding the L- to H-mode transition via periodic turbulence suppression in limit-cycle oscillations (LCOs), consistent with predator–prey dynamics. The final transition to edge-localized mode-free H-mode occurs after the equilibrium E × B flow shear increases due to ion pressure profile evolution. ZFs are also observed to initiate formation of an electron internal transport barrier (ITB) at the q = 2 rational surface via local suppression of electron-scale turbulence. Multi-channel Doppler backscattering (DBS) has revealed the radial structure of the ZF-induced shear layer and the E × B shearing rate, ω_E×B, in both barrier types. During edge barrier formation, the shearing rate lags the turbulence envelope during the LCO by 90°, transitioning to anti-correlation (180°) when the equilibrium shear dominates the turbulence-driven flow shear due to the increasing edge pressure gradient. The time-dependent flow shear and the turbulence envelope are anti-correlated (180° out of phase) in the electron ITB. LCOs with time-reversed evolution dynamics (transitioning from an equilibrium-flow dominated to a ZF-dominated state) have also been observed during the H–L back-transition and are potentially of interest for controlled ramp-down of the plasma stored energy and pressure (normalized to the poloidal magnetic field)more »« less
Cited by 32
https://doi.org/10.1088/0029-5515/54/7/073012

Full Text Available
The Center for Momentum Transport and Flow Organization in Plasmas - Final Scientific Report

Technical Report Munsat, Tobin

Overview of University of Colorado Efforts: The University of Colorado group has focused on two primary fronts during the grant period: development of a variety of multi-point diagnostic and/or imaging analysis techniques, and momentum-transport related experiments on a variety of devices (NSTX at PPPL, CSDX at UCSD, LAPD at UCLA, DIII-D at GA). Experimental work has taken advantage of several diagnostic instruments, including fast-framing cameras for imaging of electron density fluctuations (either directly or using injected gas puffs), ECEI for imaging of electron temperature fluctuations, and multi-tipped Langmuir and magnetic probes for corroborating measurements of Reynolds and Maxwell stresses. Modemore »« less
https://doi.org/10.2172/1251615

Full Text Available
Long-lived predator-prey dynamics in the pedestal of near-zero torque high performance DIII-D plasmas

Journal Article Barada, K. ; Rhodes, T. L. ; Burrell, K. H. ; ... - Physics of Plasmas

Quiescent high performance plasmas (often termed QH-mode) are attractive due to the replacement of potentially damaging energy and particle releases known as edge localized modes by relatively benign edge harmonic oscillations (EHOs). These EHOs are believed to be driven unstable by edge current and/or edge toroidal rotational shear and contribute to edge particle transport. Decreasing the applied neutral beam torque in standard QH-mode discharge leads to an improved quiescent phase of higher and wider pedestal, also known as the wide-pedestal QH-mode [Burrell et al., Phys. Plasmas 23, 056103 (2016)]. This work expands upon the observed limit cycle oscillation (LCO) dynamicsmore »« less
Cited by 5
https://doi.org/10.1063/1.5097143

Full Text Available
Turbulence and E × B flow correlations across the L-H transition in DIII-D deuterium and hydrogen plasmas

Journal Article Schmitz, Lothar - Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

The isotope dependence of the low- to high confinement-mode (L- to H-mode) transition power threshold P_LH presents significant challenges for the initial (non-nuclear) hydrogen operations phase of the international thermonuclear experimental reactor (ITER). Here, we examine the isotope dependence of turbulence and E × B flow correlation properties in the L-mode edge plasma, leading up to the L-H transition. At marginal auxiliary power (near P_LH), turbulence is initially suppressed periodically during limit cycle oscillations (LCO) that precede the transition to sustained H-mode confinement. Here, we present evidence that the long-range (toroidal) correlation of the E × B edge plasma flowmore »« less
https://doi.org/10.1098/rsta.2021.0237

Full Text Available
Mean flows and blob velocities in scrape-off layer (SOLT) simulations of an L-mode discharge on Alcator C-Mod

Dataset Russell, D. A. ; Myra, J. R. ; D’Ippolito, D. A. ; ...

Two-dimensional scrape-off layer turbulence (SOLT) code simulations are compared with an L-mode discharge on the Alcator C-Mod tokamak [M. Greenwald, et al., Phys. Plasmas 21, 110501 (2014)]. Density and temperature profiles for the simulations were obtained by smoothly fitting Thomson scattering and mirror Langmuir probe (MLP) data from the shot. Simulations differing in turbulence intensity were obtained by varying a dissipation parameter. Mean flow profiles and density fluctuation amplitudes are consistent with those measured by MLP in the experiment and with a Fourier space diagnostic designed to measure poloidal phase velocity. Blob velocities in the simulations were determined from themore »« less
https://doi.org/10.7910/DVN/4UNJMZ

View Dataset

Similar Records

Title: H-mode transitions and limit cycle oscillations from mean field transport equations

Abstract

Citation Formats

Role of Zonal Flow Predator-Prey Oscillations in Triggering the Transition to H-Mode Confinement journal, April 2012

Drift wave based modelling of poloidal spin-up precursor and stepwise expansion of transport barriers journal, July 2001

Fluctuation level bursts in a model of internal transport barrier formation journal, March 1999

Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices journal, May 1997

Constraints on theories provided by fast time response measurements across the L to H transition on DIII-D journal, August 1996

Bifurcation theory of poloidal rotation in tokamaks: A model for L-H transition journal, November 1989

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria journal, January 1982

Modifications in turbulence and edge electric fields at the L–H transition in the DIII‐D tokamak journal, August 1991

Neoclassical quasilinear transport theory of fluctuations in toroidal plasmas journal, January 1988

Transport processes and entropy production in toroidally rotating plasmas with electrostatic turbulence journal, February 1997

Poloidal momentum transport due to drift-waves in toroidal geometry journal, March 2004

Moment equation approach to neoclassical transport theory journal, January 1978

The effect of the radial electric field on the L–H transitions in tokamaks journal, March 1992

Mean and Oscillating Plasma Flows and Turbulence Interactions across the L − H Confinement Transition journal, February 2011

First Evidence of the Role of Zonal Flows for the L − H Transition at Marginal Input Power in the EAST Tokamak journal, September 2011

Observation of the L − H Confinement Bifurcation Triggered by a Turbulence-Driven Shear Flow in a Tokamak Plasma journal, March 2014

Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field journal, January 1973

Gyrokinetic theory and simulation of angular momentum transport journal, December 2007

Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio journal, September 1997

New Paradigm for Suppression of Gyrokinetic Turbulence by Velocity Shear journal, January 2013

A new paradigm for E × B velocity shear suppression of gyro-kinetic turbulence and the momentum pinch journal, September 2013

Neoclassical ion transport in rotating axisymmetric plasmas journal, January 1985

Fuel ion rotation measurement and its implications on H-mode theories journal, July 1994

Gyro-Landau fluid equations for trapped and passing particles journal, October 2005

Magnetic-confinement fusion journal, May 2016

H-mode access and the role of spectral shift with electrode biasing in the TCABR tokamak journal, July 2018

Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST) journal, December 2019

Role of Zonal Flow Predator-Prey Oscillations in Triggering the Transition to H-Mode Confinement
journal, April 2012

Drift wave based modelling of poloidal spin-up precursor and stepwise expansion of transport barriers
journal, July 2001

Fluctuation level bursts in a model of internal transport barrier formation
journal, March 1999

Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices
journal, May 1997

Constraints on theories provided by fast time response measurements across the L to H transition on DIII-D
journal, August 1996

Bifurcation theory of poloidal rotation in tokamaks: A model for L-H transition
journal, November 1989

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria
journal, January 1982

Modifications in turbulence and edge electric fields at the L–H transition in the DIII‐D tokamak
journal, August 1991

Neoclassical quasilinear transport theory of fluctuations in toroidal plasmas
journal, January 1988

Transport processes and entropy production in toroidally rotating plasmas with electrostatic turbulence
journal, February 1997

Poloidal momentum transport due to drift-waves in toroidal geometry
journal, March 2004

Moment equation approach to neoclassical transport theory
journal, January 1978

The effect of the radial electric field on the L–H transitions in tokamaks
journal, March 1992

Mean and Oscillating Plasma Flows and Turbulence Interactions across the $L − H$ Confinement Transition
journal, February 2011

First Evidence of the Role of Zonal Flows for the $L − H$ Transition at Marginal Input Power in the EAST Tokamak
journal, September 2011

Observation of the $L − H$ Confinement Bifurcation Triggered by a Turbulence-Driven Shear Flow in a Tokamak Plasma
journal, March 2014

Parallel velocity shear instabilities in an inhomogeneous plasma with a sheared magnetic field
journal, January 1973

Gyrokinetic theory and simulation of angular momentum transport
journal, December 2007

Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio
journal, September 1997

New Paradigm for Suppression of Gyrokinetic Turbulence by Velocity Shear
journal, January 2013

A new paradigm for E × B velocity shear suppression of gyro-kinetic turbulence and the momentum pinch
journal, September 2013

Neoclassical ion transport in rotating axisymmetric plasmas
journal, January 1985

Fuel ion rotation measurement and its implications on H-mode theories
journal, July 1994

Gyro-Landau fluid equations for trapped and passing particles
journal, October 2005

Magnetic-confinement fusion
journal, May 2016

H-mode access and the role of spectral shift with electrode biasing in the TCABR tokamak
journal, July 2018

Characteristics of an axisymmetric magnetic oscillation closely related to L-H transition on experimental advanced superconducting tokamak (EAST)
journal, December 2019